Combinatorics Seminar: Some instances of equivariant gamma-positivity in geometric combinatorics

Seminar | November 18 | 12:10-1 p.m. | 939 Evans Hall

 Christos Athansiadis, University of Athens (Greece)

 Department of Mathematics

Gamma-positivity provides a powerful method to prove unimodality for polynomials with real symmetric coefficients. It appeared in the seventies, in work of Foata and Sch"utzenberger on the Eulerian polynomials, and attracted considerable attention after work of Br"ande'n on poset Eulerian polynomials and Gal on triangulations of spheres. Gamma-positivity admits a natural equivariant generalization. This lecture will discuss some of few known instances of equivariant gamma-positivity, related to colored permutations and derangements on the enumerative side, and to barycentric and edgewise subdivisions on the geometric side. Somewhat surprisingly, the proofs involve group actions on the homology of posets.